Trinity Health, the parent company of Columbus-based Mount Carmel Health System, said Wednesday that its board had signed a non-binding letter of intent to merge with Catholic Health East, creating a 21-state Roman Catholic healthcare system. Trinity CEO Joseph Swedish would become CEO of the combined organization and Catholic Health CEO Judith Persichilli would be named executive vice president. The two nonprofits anticipate finalizing the merger in the spring. The combined nonprofit would have 82 hospitals, 89 nursing homes and affordable housing communities, and home health and hospice programs that do 2.8 million patient visits a year.